COSINE-MODULATED FIR FILTER BANKS SATISFYING PERFECT RECONSTRUCTION

It is well known that FIR filter banks, satisfying the perfect reconstruction (PR) property, can be obtained by cosine modulation of a linear-phase prototype of length N = 2M (M is the number of channels) when certain constraints are imposed on the prototype. Recently, this result was extended for the case when N = 2mM (m is an arbitrary positive integer). In this paper, we obtain a necessary and sufficient condition on the 2M polyphase components of a linear-phase prototype filter of length N = 2mM, such that the polyphase component matrix of the modulated filter bank is lossless. The losslessness of the polyphase component matrix, in turn, is sufficient to ensure that the analysis/synthesis system satisfies PR. Using this result, a new design procedure is presented (based on the two-channel lossless lattice). This enables the design of a large class of FIR-PR filter banks (and includes the N = 2M case). It is shown that this approach requires fewer parameters to be optimized than in the pseudo-QMF designs and in the lossless lattice based PR-QMF designs (for equal length filters in the three designs). This advantage becomes significant when designing long filters for large M. The design procedure and its other advantages are described in detail. Design examples and comparisons are included.